The perimeter of a sector of circle with central angle 90 is 25 cm Find the area of minor - Maths - Areas Related to Circles

Question

The perimeter of a sector of circle with central angle 90 is 25 cm
Find the area of minor segment

Josepaul Paulachan · Accepted Answer

Let r be the radius of a sector of a circle with center at O.

$L e n g t h o f t h e a r c A C B = l = \frac{θ}{360 °} \times 2 πr = \frac{90}{360} \times 2 \times \frac{22}{7} \times r = \frac{11 r}{7} cm$

perimeter of the sector AOBCA = 25 cm

r + r + l = 25 ⇒ 2r + $\frac{11 r}{7}$ = 25 ⇒ r = 7 cm

area of the minor segment ABCA = Area of the sector AOBCA - area of Δ AOB

$= \frac{π r^{2}}{4} - \frac{1}{2} \times O B \times O A = \frac{22 \times 49}{7 \times 4} - \frac{1}{2} \times 7 \times 7 = \frac{77}{2} - \frac{49}{2} = \frac{28}{2} = 14 {c m}^{2}$

Regards

The perimeter of a sector of circle with central angle 90 is 25 cm. Find the area of minor segment